1540s, "to dash, plunge, flop," perhaps from Scandinavian (compare dialectal Swedish flunsa "to plunge," Norwegian flunsa "to hurry, work hurriedly," but first record of these is 200 years later than the English word), said to be of imitative origin. Spelling likely influenced by bounce. Notions of "anger, impatience" began to adhere to the word 18c. Related: Flounced; flouncing. As a noun from 1580s in reference to a sudden fling or turn of the body; by mid-18c. especially as expressing impatience or disdain.
"deep ruffle on the skirt of a dress," 1713, from Middle English frounce "pleat, wrinkle, fold" (late 14c.), from Old French fronce "line, wrinkle; pucker, crease, fold," from Frankish *hrunkjan "to wrinkle," from Proto-Germanic *hrunk-, from PIE root *sker- (2) "to turn, bend." Influenced in form by flounce (v.). The verb meaning "arrange in flounces" is from 1711.